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For testing! Again!

Internet congestion control aims to achieve efficient resource utilization, acceptable packet loss and stable operation.

At the early stage of Internet, Transmission Control Protocol (TCP) played the role of providing reliable end to end connections and handling the congestion control problem. TCP uses a congestion window which adopt Additive Increasing Multiplicative Decreasing (AIMD) algorithm to limit the number of packet that can be sent at each Round Trip Propagation Time (TRPT). However, this control mechanism is only effective at sender side in the scope of each TCP connection. At link side, the traditional algorithm for congestion control is Drop-Tail (DT). Data packets form a FIFO queue at routers' ingress, DT drops the packets only if buffer overflows. DT is intuitive but can easily lead to TCP synchronization. Therefore, Active Queue Management is proposed to enhance the management of congestion at link side. AQM improves the performance by trigger packets' dropping before buffer overflows.

Random Early Detection (RED) \cite{RFC2309} is one recommended realization of AQM. RED monitors the average queue size and drops the incoming packet at a certain probability. This dropping probability is adjusted according to the average queue size: the larger queue size is, the higher the dropping probability is (To be more rigorous, the dropping probability is piecewise linear). Using control theory is another way in TCP congestion control. Hollot et al. \cite{Hollot2001} proposed a PI controller and gave guidelines to design stable PI controllers. The authors of \cite{Ryu2003} proposed a PID controller for congestion management. Compared with PI controller, PID adds a derivative part which could predict the incipient congestion. PI/PID controllers improve the performance by decoupling the dropping probability and congestion measurement. Also, close-loop feedback control mechanism improves the stability of the system.

AQM has been a very active research area, many AQM schemes have been proposed (see for example \cite{LQR,REM,DRED,Pole,Blue,ARED,RED,AVQ,nonlinear,large-delay,PD-RED,PD,JSUN,Green,RAQM} and reference therein). However, the many published AQM proposals fail to achieve optimal congestion control operation because they use fixed parameters, which is inadequate because the network state varies with time. Accordingly, an intelligent AQM controller is required for the Internet, which however is complex, highly nonlinear and time varying.

In the past few decades, extensively research has been carried on neural networks, which show proactive aspect of adaptive control. Neural networks have the remarkable ability of self-study and self-adapt. Neural systems have been successfully applied and have been proven effective in many industrial systems, such as \cite{Rigators2008, Suresh2008, Theodoridis2010, Coward2001}. More important, neural systems show great suitability in controlling non-linear system. Internet is sophisticate and non-linear, it is a good practice to implement neural system on the congestion control issue of Internet. Recently, Hariri and Sadati \cite{Hariri2007} proposed NN-RED. Motivated by these examples, we propose in this paper\footnote{A conference version of this paper has been presented in IFIP Networking 2007 \cite{sun-IFIP}.} a novel neuron-based AQM scheme.  It is called {\em Adaptive Neuronal AQM} (AN-AQM). We apply the ideas of \cite{neuron_pid1,neuron_pid4}, where an adaptive neuronal PID controller is designed for a multi-model plant. Extensive simulation results over a wide range of scenarios show that AN-AQM can control queue length and achieves fast queue-length convergence to a desirable target with small queue length jitter. These performance attributes are still maintained following significant changes to network conditions, even for long-delay networks. It will be demonstrated by extensive simulations that AN-AQM is more efficient and stable than other well-known AQM schemes.

The remainder of the paper is organized as follows. In Section \ref{scheme} (Section II), we describe the AN-AQM scheme in details. Then, in Section \ref{Simu} (Section III), we present simulation results to demonstrate that AN-AQM is effective, robust and outperforms other well-known AQM schemes. In Section \ref{Robust} (Section IV), we show the parameter robustness of AN-AQM. Finally, we conclude the paper in Section \ref{concl} (Section V).

\begin{thebibliography}{1}

\bibitem{Ott1999}
T.~J. Ott, T.~V. Lakshman, and L.~H. Wong, ``{SRED}: stabilized {RED},'' in
  \emph{Proc.IEEE INFOCOM '99}, vol.~3, New York, USA, Mar. 1999, pp.
  1346--1355.

\bibitem{Aweya2001}
J.~Aweya, M.~Ouellette, and D.~Y. Montuno, ``A control theoretic approach to
  active queue management,'' \emph{Computer Networks}, vol.~36, no. 2-3, pp.
  203--235, 2001.

\bibitem{Lin1997}
D.~Lin and R.~Morris, ``Dynamics of random early detection,'' in
  \emph{Proceedings of the ACM SIGCOMM '97}, Cannes, France, pp. 127--137.

\bibitem{Feng2001}
W.-C. Feng, D.~D. Kandlur, D.~Saha, and K.~G. Shin, ``Stochastic fair blue: a
  queue management algorithm for enforcing fairness,'' in \emph{Proc. IEEE
  INFOCOM 2001}, vol.~3, Anchorage, Alaska USA, Apr. 2001, pp. 1520--1529.

\bibitem{Hollot2001}
C.~V. Hollot, V.~Misra, D.~Towsley, and W.-B. Gong, ``On designing improved
  controllers for {AQM} routers supporting {TCP} flows,'' in \emph{Proc. IEEE
  INFOCOM 2001}, vol.~3, Anchorage, Alaska USA, Apr. 2001, pp. 1726--1734.

\bibitem{Ryu2003}
S.~Ryu, C.~Rump, and C.~Qiao, ``A predictive and robust active queue management
  for {Internet} congestion control,'' in \emph{Proc. IEEE ISCC 2003}, vol.~2,
  Kemer Antalya, Turkey, Jun./Jul. 2003, pp. 991--998.

\bibitem{Rigators2008}
G.~G. Rigators, ``Adaptive fuzzy control with output feedback for
  ${H}_{\infty}$ tracking of {SISO} nonlinear systems,'' \emph{International
  Journal of Neural Systems}, vol.~18, no.~4, pp. 305--320, 2008.

\bibitem{Suresh2008}
S.~Suresh, N.~Kannan, N.~Sundarajan, and P.~Saratchandran, ``Neural adaptive
  control for vibration suppression in composite fin-tip of aircraft,''
  \emph{International Journal of Neural Systems}, vol.~18, no.~3, pp. 219--231,
  2008.

\bibitem{Theodoridis2010}
D.~Theodoridis, Y.~Boutalis, and M.~Christodoulou, ``Indirect adaptive control
  of unknown multi variable nonlinear systems with parametric and dynamic
  uncertainties using a new neuro-fuzzy system description,''
  \emph{International Journal of Neural Systems}, vol.~20, no.~2, pp. 129--148,
  2010.

\bibitem{Coward2001}
A.~Coward, T.~Gedeon, and W.~Kenworthy, ``Application of the recommendation
  architecture to telecommunications network management,'' \emph{International
  Journal of Neural Systems}, vol.~11, no.~4, pp. 323--327, 2001.

\bibitem{Hariri2007}
B.~Hariri and N.~Sadati, ``{NN-RED}: an {AQM} mechanism based on neural
  networks,'' \emph{Electronics Letters}, vol.~43, no.~19, pp. 1053--1055, Sep.
  2007.

\bibitem{Du2004}
Y.-P. Du and N.~Wang, ``A {PID} controller with neuron tuning parameters for
  multi-model plants,'' in \emph{Machine Learning and Cybernetics, 2004.
  Proceedings of 2004 International Conference on}, vol.~6, Shanghai, China,
  Aug., pp. 3408--3411.

\bibitem{Zhang2000}
J.~Zhang, S.~Wang, and N.~Wang, ``A novel intelligent coordination control
  system for a unit power plant,'' in \emph{Intelligent Control and Automation,
  2000. Proceedings of the 3rd World Congress on}, vol.~1, Hefei, China,
  Jun./Jul. 2000, pp. 313--317.

\bibitem{LQR} D. Agrawal and F. Granelli, ``Redesigning an active
queue management system,'' \emph{Proc. IEEE GLOBECOM 2004}, pp.
702--706, 2004.

\bibitem{REM} S. Athuraliya, S. H. Low, V. H. Li and Q. Yin, ``REM: Active queue
management,'' \emph{IEEE Network Mag.}, vol. 15, no. 3, pp. 48--53,
2001.

\bibitem{DRED} J. Aweya, M. Ouellette and D. Y.
Montuno, ``A control theoretic approach to active queue
management,'' \emph{Computer Networks}, vol. 36, nos. 2-3, pp.
203--235, 2001.

\bibitem{RFC2309} B. Braden, et al., ``Recommendations on queue
management and congestion avoidance in the Internet,'' IETF RFC2309,
1998.

\bibitem{Pole} Q. Chen and O. W. W. Yang, ``On designing self-tuning controller for
AQM routers supporting TCP flows based on pole placement,''
\emph{IEEE Journal on Selected Areas in Communications}, vol. 22,
no. 10, pp. 1965--1974, 2004.

\bibitem{neuron_pid1} Y. Du and N. Wang, ``A PID controller with neuron tuning parameters for multi-model
plants,'' \emph{ Proceedings of 2004 International Conference on
Machine Learning and Cybernetics}, vol. 6, pp. 3408--3411, 2004.

\bibitem{Blue}  W. Feng, D. Kandlur, D. Saha and K. Shin,
``The Blue queue management algorithms,'' {\em IEEE/ACM Trans. on
Networking}, vol. 10, no. 4, pp. 513--528, Aug. 2002.

\bibitem{ARED} S. Floyd, R. Gummadi and S.
Shenker, ``Adaptive RED: An algorithm for increasing the robustness
of RED's active queue management,'' available at
http://www.icir.org/floyd/red.html.

\bibitem{RED} S. Floyd and V. Jacobson, ``Random
early detection gateways for congestion avoidance,'' \emph{IEEE/ACM
Trans. on Networking}, vol. 1, no. 4, pp. 397--413, Aug. 1993.

\bibitem{PI} C. V. Hollot,  V. Misra, D.
Towsley and W. Gong, ``On designing improved controllers for AQM
routers supporting TCP flows,'' \emph{Proc. IEEE INFOCOM 2001},
Anchorage, Alaska, April 2001, vol. 3, pp. 1726--1734.

\bibitem{AVQ} S. S. Kunniyur and R. Srikant,
``An adaptive virtual queue (AVQ) algorithm for active queue
management,'' {\em IEEE/ACM Trans. on Networking}, vol. 12, no. 2,
pp. 286--299, April 2004.

\bibitem{leng} S. Leng, K. R.
Subramanian, N. Sundararajan and P. Saratchandran, ``Novel neutral
network approach to call admission control in high-speed networks,''
{\em International Journal of Neural Systems}, vol. 13, no. 4, pp.
251--262, August 2003.

\bibitem{NS}
The NS simulator and the documentation, available at
$<$\emph{http://www.isi.edu/nsnam/ns/}$>$.

\bibitem{nonlinear}  P. Ranjan, E. H. Abed and R. J. La, ``Nonlinear instabilities in TCP-RED,"
\emph{IEEE/ACM Trans. on Networking}, vol. 12, no. 6, pp.
1079--1092, 2004.

\bibitem{large-delay} F. Ren, C. Lin and B. Wei, ``A
robust active queue management algorithm in large delay networks,''
\emph{Computer Communications}, vol. 28, no. 5, pp. 485--493, 2005.

\bibitem{ros} E. Ros, F. J. Pelayo, D. Palomar, I. Rojas, J. L.
Bernier and A. Prieto, ``Stimulus correlation and adaptive motion
detection using spiking neurons,'' {\em International Journal of
Neural Systems}, vol. 9, no. 5, pp. 485- 490, October 1999.

\bibitem{PD-RED} J. Sun, K. T. Ko, G. Chen, S. Chan
and M. Zukerman, ``PD-RED: to Improve the Performance of RED,''
\emph{IEEE Communications Letters}, vol. 7, no. 8, pp. 406--408,
August 2003.

\bibitem{PD} J. Sun, G. Chen, K. T. Ko, S. Chan and M.
Zukerman, ``PD-Controller: A new active queue management scheme,''
\emph{proc. IEEE Globecom},  San Francisco, 2003, vol. 6, pp.
3103--3107.

\bibitem{JSUN}J. Sun, M. Zukerman, K. T. Ko, G. Chen and S. Chan, ``Effect of
large buffers on TCP queueing behavior,'' \emph{ Proc. IEEE
INFOCOM}, vol. 2, pp. 751-761, 2004.
\bibitem{sun-ITC} J. Sun and M. Zukerman, ``Improving
RED by a neuron controller'', {\em Proceedings of ITC 20}, Ottawa,
Canada, 2007.

\bibitem{sun-IFIP} J. Sun and M. Zukerman, ``An
adaptive neuron AQM for a stable Internet,'' {\em  Proceedings of
IFIP Networking 2007}, Atlanta, May 2007.

\bibitem{Green} B. Wydrowski and M. Zukerman, ``GREEN: An active queue management
algorithm for a self managed Internet,'' {\em Proceedings of ICC
2002}, New York, 2002, vol. 4, pp. 2368--2372.

\bibitem{RAQM} C. Wang, B. Li, Y. T. Hou, K. Sohraby and K. Long,
``A stable rate-based algorithm for active queue management,''
\emph{Computer Communications}, vol. 28, pp. 1731--1740, 2005

\bibitem{QoS}
B. Wydrowski and M. Zukerman, ``QoS in best-effort networks,'' {\em
IEEE Communications Magazine}, vol. 40, no. 12, pp. 44--49, Dec.
2002.

\bibitem{neuron_pid4} J. Zhang, S. Wang and N. Wang ``A
new intelligent coordination control system for a unit power plant
,'' \emph{Proceedings of the 3rd World Congress on Intelligent
Control and  Automation}, pp. 313--317, 2000.
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\end{thebibliography}

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